Cosmology with Large-scale Structure of the Universe Eiichiro - - PowerPoint PPT Presentation
Cosmology with Large-scale Structure of the Universe Eiichiro Komatsu (Texas Cosmology Center, UT Austin) Korean Young Cosmologists Workshop, June 27, 2011 Cosmology Update: WMAP 7-year+ Standard Model H&He = 4.58% (0.16%)
Eiichiro Komatsu (Texas Cosmology Center, UT Austin) Korean Young Cosmologists Workshop, June 27, 2011
years (±0.11 billion years)
“ScienceNews” article on the WMAP 7-year results
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(Panel Report, Page T
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(Panel Report, Page T
Inflation Dark Energy Dark Matter Neutrino Mass
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(Panel Report, Page T
Inflation Dark Energy Dark Matter Neutrino Mass
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redshift range
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Hlozek et al., arXiv:1105.4887 non-linear P(k) at z=0 linear P(k)
Matter density fluctuations measured by various tracers, extrapolated to z=0 CMB, z=1090 (l=2–3000) Galaxy, z=0.3 Gas, z=3
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non-linear P(k) at z=0 linear P(k)
Matter density fluctuations measured by various tracers, extrapolated to z=0 CMB, z=1090 (l=2–3000) Galaxy, z=0.3 Gas, z=3
Primordial spectrum, Pprim(k)~kns
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non-linear P(k) at z=0 linear P(k) asymptotes to kns(lnk)2/k4
T(k): Suppression of power during the radiation- dominated era.
Primordial spectrum, Pprim(k)~kns
The suppression depends
P(k)=A x kns x T2(k)
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bar by a factor of ~4.
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primordial tilt, ns, and the tensor-to-scalar ratio, r.
5-year limit.
power spectrum: ns=0.968±0.012 (68%CL)
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Komatsu et al. (2011)
r = (gravitational waves)2 / (gravitational potential)2 Planck?
(l=3000).
smaller scales.
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non-linear P(k) at z=0 linear P(k)
Matter density fluctuations measured by various tracers, extrapolated to z=0 CMB, z=1090 (l=2–3000) Galaxy, high-z Gas, z=3
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enough.
ns, i.e., deviation of Pprim(k) from a pure power-law, then we need the small-scale data.
quite powerful (Takada, Komatsu & Futamase 2006)
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close to Gaussian.
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= <ζk1ζk2ζk3> = (amplitude) x (2π)3δ(k1+k2+k3)F(k1,k2,k3)
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model-dependent function
k1 k2 k3 Primordial fluctuation
MOST IMPORTANT
squeezed limit is given by
Maldacena (2003); Seery & Lidsey (2005); Creminelli & Zaldarriaga (2004)
* for which the single field is solely responsible for driving inflation and generating observed fluctuations.
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simple single-field inflation models: 1–ns≈r≈fNL
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Komatsu et al. (2011)
Pζ(k1)Pζ(k2)Pζ(k3)+cyc.] +τNL[Pζ(k1)Pζ(k2)(Pζ(| k1+k3|)+Pζ(|k1+k4|))+cyc.]} k3 k4 k2 k1
k2 k1 k3 k4
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from WMAP 7-year are consistent with single-field or multi- field models.
with the future.
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ln(fNL) ln(τNL) 74 3.3x104
(Smidt et
x0.5
anything after
survived the test (for the moment: the future galaxy surveys can improve the limits by a factor of ten). ln(fNL) ln(τNL) 10 600
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x0.5
field is dead.
detected, in accordance with multi- field models: τNL>0.5 (6fNL/5)2 [Sugiyama, Komatsu & Futamase (2011)] ln(fNL) ln(τNL) 600
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30 x0.5
field is dead.
detected, inconsistent with the multi-field bound.
this bound may not be completely general) BOTH the single-field and multi-field are gone. ln(fNL) ln(τNL) 30 600
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x0.5
3D information. (CMB is 2D, so the number of Fourier modes is limited.)
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linear, so perhaps it is less clean?
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MOST IMPORTANT
elongated triangles.
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less enhancement along the elongated triangles.
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clearly distinguishable from other non-linear/ astrophysical effects.
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Sefusatti & Komatsu (2007); Jeong & Komatsu (2010)
SDSS-LRG)
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(1) Luminosity Distances (Type Ia supernovae) (2) Angular Diameter Distances (BAO, CMB) simultaneously is qualified for being called “Dark Energy.”
modified gravity, and (c) extreme inhomogeneity.
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WMAP7+
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0.2 2 6 1090
Type 1a Supernovae Galaxies (BAO) CMB
0.02
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measure DA. What determines d?
0.2 2 6 1090
Galaxies CMB
0.02
dBAO dCMB
θ θ
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determines the physical size of typical spots, dCMB?
θ θ~the typical size of hot/cold spots θ θ θ θ θ θ θ
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physical distance traveled by the sound wave from the Big Bang to the decoupling of photons at zCMB~1090 (tCMB~380,000 years).
where cs(t) is the time-dependent speed of sound
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lCMB=302.69±0.76
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lCMB=πDA(zCMB)/ds(zCMB) with zEQ & Ωbh2.
Chain from WMAP 3yr (Spergel et al. 2007)
lCMB=301.8±1.2
1-Ωm-ΩΛ = 0.3040Ωm +0.4067ΩΛ
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0.0 0.5 1.0 1.5 2.0 M 0.0 0.5 1.0 1.5 2.0
(M,) = (0.27,0.73) Total=1
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galaxy distribution... 2dFGRS
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function yields oscillations in Fourier space. (1+z)dBAO Percival et al. (2006) Okumura et al. (2007)
Position Space Fourier Space
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traveled by the sound wave from the Big Bang to the decoupling of baryons at zBAO=1020.5±1.6 (c.f., zCMB=1091±1).
accidentally happens to be the case for our Universe.
greater than unity, zBAO>zCMB. Since our Universe happens to have Ωbh2=0.022, zBAO<zCMB. (ie, dBAO>dCMB)
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curvature≠0!
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Komatsu et al. (2009)
it can be used to measure not only DA(z), but also the expansion rate, H(z), directly, at that redshift.
=> DA(z) = ds(zBAO)/θ
=> H(z) = cΔz/[(1+z)ds(zBAO)]
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Two-point correlation function measured from the SDSS Luminous Red Galaxies (Gaztanaga, Cabre & Hui 2008) (1+z)ds(zBAO)
θ = ds(zBAO)/DA(z) cΔz/(1+z) = ds(zBAO)H(z)
Linear Theory SDSS Data
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Percival et al. (2010)
2dFGRS and SDSS main samples SDSS LRG samples
(1+zBAO)ds(zBAO)/DV(z)
Ωm=0.278, ΩΛ=0.722
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0.2 0.3 0.4
Since the current data are not good enough to constrain DA(z) and H(z) separately, a combination distance, DV(z), has been constrained.
great for fixing curvature, but not good for fixing w
for fixing w, but this would change as more BAO data (especially at higher redshifts) become available.
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Komatsu et al. (2011)
Komatsu et al. (2011)
w0=–1 and wa=0, are perfectly consistent with data.
to change at some point...
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500 1000
500 1000
Sloan Digital Sky Survey
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Small Scale Large Scale
500 1000
500 1000
HETDEX
10x more galaxies observed 3x larger volume surveyed Will survey the previously unexplored discovery space
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Small Scale Large Scale
contained in the galaxy power spectrum!
leads to a substantial improvement in the precision of distance and expansion rate measurements.
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the determinations of DA & H by more than a factor of two.
than a factor of four. Shoji, Jeong & Komatsu (2008)
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come from?
This is the most important component for the success of the HETDEX survey.
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distortion - we will include this for the full analysis; we ignore it here for simplicity), the distribution of the power should be isotropic in Fourier space.
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transverse wavenumber
parallel wavenumber
If DA and H are correct: kpara kperp If DA is wrong: kperp If H is wrong: kperp
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transverse wavenumber
parallel wavenumber
If DA and H are correct: kpara kperp If DA is wrong: kperp If H is wrong: kperp kperp If DA and H are wrong:
to determine DA and H separately; however, it gives a measurement of DAH.
information, and marginalizing
distortion, we get the solid contours in the figure.
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the distribution of the power anisotropic. Would it spoil the utility of this method?
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f is marginalized over. f is fixed.
perturbations at z~1090. Let’s call that Rk. The relation to the density fluctuation is
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where kWMAP=0.027 Mpc–1
g(z)=(1+z)D(z)
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Flat Universe Non-flat Univ.
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Alexey Vikhlinin, from a slide presented at the IPMU Dark Energy Conference in Japan, June 2009
g(z)=
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the matter power spectrum on small scales (k>0.1 h Mpc–1).
remember:
power spectrum at k>0.1 h Mpc–1 is suppressed by ~7%.
easily!
For 10x the number density of HETDEX
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masses!
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cosmic variance limited regime shot noise limited regime
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major breakthroughs in any of the above questions.
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